Singular Solutions of Elliptic Equations with Iterated Exponentials

  title={Singular Solutions of Elliptic Equations with Iterated Exponentials},
  author={Marius Ghergu and Olivier Goubet},
  journal={The Journal of Geometric Analysis},
We construct positive singular solutions for the problem $$-\Delta u=\lambda \exp (e^u)$$ - Δ u = λ exp ( e u ) in $$B_1\subset {\mathbb {R}}^n$$ B 1 ⊂ R n ( $$n\ge 3$$ n ≥ 3 ), $$u=0$$ u = 0 on $$\partial B_1$$ ∂ B 1 , having a prescribed behaviour around the origin. Our study extends the one in Miyamoto (J Differ Equ 264:2684–2707, 2018) for such nonlinearities. Our approach is then carried out to elliptic equations featuring iterated exponentials. 
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